If imitation is the sincerest form of flattery, then Rafael Benítez must have spent Sunday afternoon blushing like a schoolgirl. Six and a half years on from that night in Istanbul, when his Liverpool team came back from three goals down to beat Milan in the Champions League final, the Rossoneri staged a re-enactment of which any historical society could be proud. Sure, one or two details had been tweaked – this time, after all, Milan won – but few others could have pulled off such an unbalanced performance with similar aplomb.

Three-nil down at half-time, the champions had been woeful. Guillermo Giacomazzi had been allowed a clear run at a Carlos Grossmüller cross to head home the opener, while the latter had slotted home Lecce's third after having the ball essentially passed to him by Milan's Luca Antonini inside the area. Their second goal might have been the result of an unfairly awarded penalty but Daniele Corvia would never have had the opportunity to throw himself to the ground before Christian Abbiati had the goalkeeper not first dropped the ball needlessly at the striker's feet.

At that stage it was hard to envisage any way back in an away fixture that Milan had not won since 2002. Inside the visitors' dressing room the manager, Massimiliano Allegri, chose not to chastise his players. Instead he went around them one-by-one, offering quiet words of encouragement – insisting that this game was not yet lost – but Kevin-Prince Boateng had no need for a pep-talk. The manager's message was right there in front of him – tattooed across the back of his own left hand. "Believe."

Boateng had begun the game as a substitute, ostensibly over a fitness complaint, though various reporters have speculated that his omission from the starting line-up was more a comment on the player's mental focus than any physical ailment. The Ghanaian has developed a reputation over the past year as one who is perhaps a little too fond of the Milan nightlife. "Good night in Portuguese is said 'boa noite'," notes Sebastiano Vernazza in today's Gazzetta dello Sport. "Milan's 'Boa' has been allowing himself a few good nights in the city."

Some have even sought to highlight the player's famous Moonwalk title celebrations as a turning point in the player's mindset. In truth that seems a bit tenuous – since the player had already been reprimanded along with Urby Emanuelson and Alexander Merkel for indulging in a big night out in March before an away trip to Palermo. But Corriere della Sera was not alone today in suggesting that his recent appointment of two personal bodyguards may be indicative of a man who is allowing the fame to go to his head.

The player himself has admitted in the past to not being as diligent as he might at times in his career. "I didn't even train sometimes I just thought 'yeah, I'm a big player now,'" he told Sabotage Times last year. "I took everything easy and didn't work hard and then I did the same when I got to Spurs. I thought they've paid £8m for me so of course they're going to play me."

But while Allegri and his staff are the only ones who truly know what goes on in training at Milanello, the player had seemed perfectly focused as he scored in the win over Bate Borisov on Wednesday. And as the journalist Carlo Pellegatti was pointed out to fellow reporters in the press box on Sunday, "[Ruud] Gullit chased after women like a madman. As long as he was still Gullit, there was no problem. Everyone would praise him, saying: 'Well done Ruud, do what seems right to you.'" It was only when the goals dried up, that the mood turned.

Either way, there certainly seemed little evidence of any physical fitness problem as Boateng hoicked an entire team on to his back and set about dismantling Lecce. Within six minutes of coming on he had already achieved more than the rest of Milan's front line put together, with three shots and a delicious goal, the ball swerving violently off his left boot and into the far top corner as he met an Antonio Cassano cross inside the area. Within 18 minutes he had a hat-trick and Milan were level.

The second goal was not half bad either, exploding off Boateng's right and into the roof of the net from just outside the D. By the time he had forced in the third from close range, Lecce's spirit was broken. Milan's eventual winner, a header from Mario Yepes, felt entirely inevitable.

"Was I angry [at being left on the bench]?" mused Boateng – apparently only the second player in the history of Serie A to score a hat-trick after coming on as a substitute. "I never look backwards, I am happy to have scored three goals and to have taken the match-ball home with me but above all I am happy with the team's win. It was an incredible match, but now we are closer to the leaders."

Technically he was incorrect – since Milan finished the weekend precisely the same number of points behind first-placed Udinese as they had been at the beginning of the weekend. The Friuliani had been joint-top alongside Juventus for a couple of weeks but moved into sole possession of first place by beating Novara 3-0 after Antonio Conte's team had drawn with Genoa. If there are those who see the sign of champions in Milan's rousing comeback, then it is also worth raising a piece of received wisdom from American sports: defence wins championships.

Through their first seven games, Francesco Guidolin's team have conceded just a single goal and yesterday they held firm against a Novara side who had come into the game as the league's joint-top scorers so far this season. That would appear quite the departure for a team who became renowned last season for their swashbuckling and, at times reckless, attacking football though with Samir Handanovic between the sticks it ought not to come as so great a surprise.

Brilliance was not required of the Slovenian yesterday – though Novara did have more shots on target than their hosts – but few goalkeepers in any league have been in better form over the past 12 months. Although much was written about his aptitude for saving penalties last season – when he stopped a record-breaking six – few seemed to take much notice of the fact that last season he also went a league-best 704 minutes without conceding a goal of any kind at a key point of the season from February into mid-March.

The defence too, though, have been impressive – handling the departures of Cristián Zapata and Gokhan Inler, previously their shield at the base of the Udinese midfield, far more easily than any could have imagined. But the manager Guidolin was dismissive when asked if his team could contend for the Scudetto. He had spent a part of the second half gesturing to his own team's fans to ease off on the songs about even being top of the league now.

You could hardly blame them, given that this is now the first time in 11 seasons that Udinese have had first place all to themselves. But after Milan's performance in the lunchtime game, you could also understand why the manager might feel that not even a three-goal lead should be taken for granted.

Talking points

• Udinese are also looking in very good shape in the Europa League, with seven points from their first three games, and it is Italy's only other remaining representative in that competition who now sit second in Serie A. Lazio have done rather worse in Europe, a draw in Zurich on Thursday leaving them with just two points in the competition, but at home they followed up last week's derby win with a comfortable victory at Bologna. Their manager, Edy Reja, was not quite as reticent as Guidolin to talk about the title, though he too insisted this was not the time to get carried away. "Let's wait until the midway point to see who are the forces leading the way in the league," he said.

• A 1-0 win over Chievo might not seem like much to shout about for Inter, but Thiago Motta's first-half winner for the Nerazzurri was remarkably the first goal they have scored at home all season. On the week of his 60th birthday, it is the gift Claudio Ranieri had most hoped for.

• The wait is over: Erik Lamela has arrived, and what a first appearance it was for the 19-year-old, marked with an excellent goal – arced with precision across the goalkeeper Alexandros Tzorvas and into the far corner of the net – that would prove enough to seal a home win for Roma over Palermo. Reasonable judgements cannot be made on the strength of one performance, but Roma will have seen enough to at least hope that he can provide the spark of creativity that Luis Enrique's team has thus far been missing.

• The new Juventus Stadium has attracted much praise since its opening, but since Thursday it has been drawing the opposite kind of attention after Turin authorities opened an investigation into its safety. It has been alleged that the steel used in the construction did not meet EU standards, and subsequently speculated that the stadium may not be safe. Juventus have firmly rejected that last claim and received approval from the local authorities to press ahead with this weekend's home game over Genoa. Fans clearly were not perturbed, as the stadium was once again full. They will, however, have been frustrated to see their team blow two leads to a fourth draw in five games.